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Observation-Based Physics for the Third Generation Wave Models Alexander Babanin, Ian Young, Erick Rogers and Stefan Zieger Centre for Ocean Engineering, Science and Technology Swinburne University, Melbourne Australian National University, Canberra Naval Research Laboratory, MS, USA Hobart, Australia May, 2014

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Radiative Transfer Equation is used in spectral models for wave forecast Describes temporal and spatial evolution of the wave energy spectrum E(k,f t,x) S tot all physical processes which affect the energy transfer S in energy input from the wind S ds dissipation due to wave breaking S nl nonlinear interaction between spectral components S bf dissipation due to interaction with the bottom

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Motivation physics (parameterisations of the source terms) was cursory had not been updated for some 20 years was not based on observations bulk calibration Requirements for the modern-day models: more accurate forecast/hindcast being used in the whole range of conditions, from swell to hurricanes coupling with weather, ocean circulation and climate models

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Lake George experiment sponsored by ONR 20 km x 10km uniform finite water depth (0.3m - 2.2m) steep waves f p > 0.3 Hz strongly forced waves 1 < U/c p < 8 source functions measured

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following the waves

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The full flow separation

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The parameterisation, growth rate

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Flow separation due to breaking f) = 0 (f)(1+b T )

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Wind Input S in Donelan, Babanin, Young and Banner (Part I, JTEC, 2005; Part II, JPO, 2006, Part III, JPO, 2007) the parameterisation includes very strongly forced and steep wave conditions, the wind input for which has never before been directly measured in field conditions the parameterisation includes very strongly forced and steep wave conditions, the wind input for which has never before been directly measured in field conditions new physical features of air-sea exchange have been found: new physical features of air-sea exchange have been found: - full separation of the air flow at strong wind over steep waves - full separation of the air flow at strong wind over steep waves - the exchange mechanism is non-linear and depends on the wave steepness - the exchange mechanism is non-linear and depends on the wave steepness - enhancement of the input over breaking waves - enhancement of the input over breaking waves = 0 (1+b T ) pressure-height decay is very rapid for strong winds young seas combination - pressure-height decay is very rapid for strong winds young seas combination

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Breaking Dissipation Breaking Dissipation S ds two passive acoustic methods to study spectral dissipation - segmenting a record into breaking and non-breaking segments - using acoustic signatures of individual bubble-formation events Babanin et al., 2001, 2007, 2010, Babanin & Young (2005), Manasseh et al. (2006), Young and Babanin (2006), Babanin (2011)

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White Cap Dissipation White Cap Dissipation S ds 1) Spectrogram method Frequency distribution of dissipation due to dominant breaking. - Cumulative effect Young and Babanin, 2006, JPO

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White Cap Dissipation White Cap Dissipation S ds 1) Segmenting the record Directional dissipation fpfp 2f p fpfp

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S ds Bubble-detection method Cumulative effect Dependence on the wind two-phase behaviour of spectral dissipation: - linear dependence of S ds on the spectrum at the peak - cumulative effect at smaller scales b T depends on the wind for U 10 > 14 m/s Manasseh et al., 2006, JTEC

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White Cap Dissipation White Cap Dissipation Sds 1)Spectrogram method Threshold behaviour of the dissipation Babanin et al., 2001, JGR Babanin & van der Weshuysen, JPO, 2008 threshold behaviour is also predicted by the modulational instability Babanin and Young, WAVES-2005

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White Cap Dissipation White Cap Dissipation S ds spectral dissipation was approached by two independent means based on passive acoustic methods threshold: if the wave energy dissipation at each frequency were due to whitecapping only, it should be a function of the excess of the spectral density above a dimensionless threshold spectral level, below which no breaking occurs at this frequency. This was found to be the case around the wave spectral peak: dominant breaking dissipation at a particular frequency above the peak demonstrates a cumulative effect, depending on the rates of spectral dissipation at lower frequencies dimensionless saturation threshold value of should be used to obtain the dimensional spectral threshold F thr (f) at each frequency f dissipation depends on the wind for U10 > 14 m/s Babanin, APS, 2009

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Methodology Important! observe known physical constrains calibrate the source functions, if necessary, separately Tsagareli et al, 2010, JPO Babanin et al., 2010, JPO

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Swell attenuation b 1 =0.002 Dissipation volumetric per unit of surface per unit of propagation distance Babanin, CUP, 2011

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Swell attenuation Young, Babanin, Zieger, JPO, 2013

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TESTING, CALIBRATION, VALIDATIONS

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Charles James, PIRSA-SARDI (UA), Spencer Gulf SWAN model, default and new physics (Rogers et al., 2012)

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Cyclone Yasi waves next to Townsville (ADCP) and Cape Cleveland (buoy) Deep water track, winds (top), waves (bottom)

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Hindcast 2006 Spatial bias in mean wave height TEST451 with BETA max =1.33 BYDRZ swell parameter b 1 =0.25E-3 TEST451 BYDRZ validations/updates if based on physics, incremental improvements of the model are possible changing a source term does not require re-turning the other source terms integrals of the sources can be used as fluxes for coupling with GCMs

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observation-based source terms Implemented in WAVEWATCH-III and SWAN Wind input (Donelan et al. 2006, Babanin et al, 2010) -weakly nonlinear in terms of spectrum -slows down at strong winds (drag saturation) -constraint on the total input in terms of wind stress Breaking dissipation (Babanin & Young 2005, Rogers et al. 2012) -threshold in terms of spectral density -cumulative effect away from the spectral peak -strongly nonlinear in terms of spectrum Non-breaking (swell) dissipation (Babanin 2011, Young et al. 2013) -interaction of waves with water turbulence Negative input (adverse or oblique winds, Donelan 1999, unpublished Lake George observations) -of principal significance for modelling waves in tropical cyclones Physical constraints (Babanin et al. 2010, Tsagareli et al. 2010)

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Where to go?

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work in progress Wave-bottom interactions (completed) Boundary layer model instead of wind input parameterisation New term for non-linear interactions (non- homogeneous, quasi-resonant, Stokes corrections, wave breaking) Wave-current interactions Wave-ice interactions

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Model Based on Full Physics Can be used for prediction of adverse events (dangerous seas, freak waves, swells, breaking, steepness, PDF tail) outputting the fluxes coupling with extreme weather (hurricane) models coupling with atmospheric and oceanic modules of GCMs, atmospheric boundary layer, ocean circulation, climate

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Input and total stress JONSWAP DHH f -4 to f -5

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Whitecapping dissipation now, coefficients a and b need to be found Young and Babanin a = 0.0069 (only one record analysed) Donelan (1998) showing the fraction of momentum (dashed line) and of energy (plain line) retained by the waves coeff. a and b based on the input/dissipation ratio